The family courts system is at breaking point due to delays caused by unrepresented litigants and overstretched judges, according to the body that represents lawyers and professionals in divorce hearings.

Jo Edwards, a solicitor and the newly appointed chair of Resolution, fears that a two-tier system of justice is emerging where private clients opt out of overcrowded, slow-moving public courts in favour of private arbitration hearings.

Cuts to legal aid have deprived separating couples of funding for representation and legal advice, leaving them to navigate their own way through the courts as they attempt to reach settlements on complex, emotional issues of child custody and division of family assets.

The result is that as many as two-thirds of cases working their way through the family courts now involve at least one side which has no lawyer to provide help, Edwards estimates. Such cases take more time because judges have to help litigants in person develop their claims.

The note of alarm Edwards is sounding may be more shrill than those of other lawyers but it is, she insists, a response to the experience of solicitors who work in family courts every day. "People are just giving up and not seeing their children because they don't know how to go about it," she said.

"We accept you can't go back to [funding family cases all the way through] but if you have a system at breaking point that will be more costly. The family courts system is very, very, very stretched. We recently met the Association of District Judges [who deal with family cases in county courts] and they were virtually holding their heads in their hands and saying it's very diffficult.

"People who represent themselves are not negotiating. They need a lot of time and help. The judges are having to draft orders which is normally done by the parties. I have heard of cases being listed eight months in advance. "

Resolution believes that providing legal aid for a single, initial meeting with a lawyer would provide separating couples with clear "signposts" about their legal options and encourage more people to use mediation as an alternative to courtroom confrontations.

The organisation is already running a pilot project along those lines for the Department of Work and Pensions in Crewe, Oxford and Newcastle, working with people who would previously have been eligible for legal aid. The number of couples attending mediation sessions plummeted last year following the removal of legal aid; divorcing couples stopped going to solicitors who would have directed them on to trained mediators.

Since April, it has been mandatory for litigants to attend a Miam (mediation, information and assessment meeting) before pursuing a court case. There are no published figures so far to demonstrate whether that has resulted in a revival in the number of mediation hearings.

Edwards, a family expert with the law firm Penningtons Manches, believes that successive governments have dodged the political responsibility of introducing no-fault divorces because they do not want to be blamed for making divorce easier.

There were 118,000 divorces in England and Wales in 2012, a small increase on the previous year's figure. The numbers peaked at more than 165,000 a year in the 1990s. The problem for those separating is compounded by the media's obsession with the divorces of multimillionaires, Edwards said.

"The only cases reported are the huge money ones which are not applicable to the man in the street. So you have lots of people representing themselves who are deriving no real guidance [about the state of the law]." People representing themselves tend also to bring along more supporters, she added, increasing the number of "raised voices" in family courts and the level of tension.

Responding to the concerns, the justice minister, Simon Hughes, said: "There have always been a significant number of people representing themselves in court — they did in around half of all private law cases in 2012 - and we provide information and guidance to help them. Judges have expertise in supporting them, for example by explaining procedures and what is expected.

"We are committed to making sure that more people make use of mediation rather than go through the confrontational and stressful experience of going to court. Millions of pounds of legal aid remains available for family mediation and for legal advice to support family mediation.

"We are closely monitoring the impact of the legal aid changes and will continue to do so. Court performance is being maintained with the average time taken to complete cases remaining steady since April 2013."